s12 - 6.045J/18.400J: Automata, Computability and...

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Unformatted text preview: 6.045J/18.400J: Automata, Computability and Complexity Nancy Lynch Homework 12 Due: May 7, 2007 Elena Grigorescu Readings: Section 9.1, 9.2 Problem 1 : Sipser 9.13 Let pad ( s,l ) be the function that adds enough copies of the symbol # to the end of the string s so that the length of the result is at least l . For any language A and function f : N → N define the language pad ( A,f ( m )) = { pad ( s,f ( m )) | where s ∈ A,m is the length of s } . Prove that if A ∈ TIME ( n 6 ) then pad ( A,n 2 ) ∈ TIME ( n 3 ). Solution 1 : Consider the following decider for pad ( A,n 2 ): M:” on input x # t use the decider for A to decide if x ∈ A if no reject; if yes, check that t = | x | 2 − | x | and output yes if so and no otherwise.” M runs in time O ( N 3 ) since now the size of the input is N = n 2 . Problem 2 : Sipser 9.14 Prove that, if NEXPTIME negationslash = EXPTIME then P negationslash = NP ....
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This note was uploaded on 08/12/2009 for the course CS 420 taught by Professor Nancylynch during the Spring '07 term at New Mexico Junior College.

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